Information Sciences and Computer Engineering, Vol. 2, No. 2, (2011) 1–6

International Journal ofInformation Sciences and Computer Engineering

j o u r n a l h o m e p a g e : http://www.ijisce.org

Design and Simulation of DC/DC Buck Converter for Stand Alone Photovoltaic EnergySystem with Lead Acid Battery Storage

Fatima Zahra Amatoul∗, Moulay Tahar Lamchich, Abdelkader Outzourhit

Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

Abstract– This paper presents the design and simulation of DC/DC buck con-verter using Matlab and Simulink. The model contains a detailed represen-tation of the solar photovoltaic (PV) array, Lead Acid battery, DC/DC con-verter, and DC load. In our studies, we conceived a PV system where the PVgenerator is the panel NA-901(WQ). The simulation has been tested on So-lar PV Module (Micro-amorphous silicon thin-film) rated 90Wpeak at 49.3V,1.83A at 25 degree Celsius and 1000W/m2 (STC). The complete model wassimulated during a variation transient in climatic conditions.

Keyword: Solar cells; photovoltaic (PV); battery; buck converter; modeling;DC-DC regulator; design; simulation.

1. Introduction

Most large photovoltaic systems are solar energy supply sys-tems, which either supply power directly to electrical equipmentor feed energy into the public electricity grid. In some smallapplications, PV (photovoltaic) systems are operated in isolatedconfiguration where a battery storage system is required. Theelectrical system powered by solar arrays requires special designconsiderations due to varying nature of the solar power resultingfrom unpredictable and sudden changes in weather conditions[1], which change the solar irradiation level as well as the celloperating temperature [2, 3].

The system under study is designed to power a 48V DC loadand require a 48V lead acid battery rated at 1100Ah. A DC loadis preferable for several reasons. First, since a photovoltaic cellproduces DC power, there is no need for an inverter to convertthe DC power to AC, as in most current PV systems. Second,LED lighting has made huge advancements, and is more efficientthan the standard incandescent bulb. Also, batteries provide DCpower, and can be easily charged by DC source. Many electricalappliances use DC power as well.

On the other hand, battery charging is very popular because ofits simplicity and versatility. Many papers on battery charginghave been written [4, 5].

∗Corresponding author:Email: fatitoul@gmail.com, Ph: +212 6647210550

The main objectives of this paper is to model and analyze thesystem, and predict the performance improvements that can beachieved by altering the system configuration to better match theload of the PV system.

This paper is organized as follows: In Section 2, The dynamicmodel and characteristics of the PV array are described. The de-sign and modelling of the buck converter will be presented inSection 3. In Section 4, the battery model based on a lead-acidbattery is presented. In Section 5, the dc-dc regulator system isdiscussed. The simulation descriptions and results will be de-scribed in Section 6. Finally the conclusions will be present inSection 7.

2. Modelling of photovoltaic system

A PV cell is a specially designed PN junction or Schottky bar-rier device. The well-known diode equation describes the opera-tion of the shaded PV cell [6].

In order to obtain an adequate output voltage, PV cells are con-nected in series to form a PV module. If higher voltages or cur-rents are not available from a single module, modules must beconnected into arrays as shown in Fig. 1. Series connections re-sult in higher voltages, while parallel connections result in highercurrents.

Fig. 1. Example of PV arrays

Model for solar PV array is developed in Simulink. The PV ar-

2 Amatoul et al./Information Sciences and Computer Engineering, Vol. 2, No. 2, 2011

ray makes use of the equations of a typical solar cell. The typicalmodel of a solar cell is shown in Fig. 2. The current and voltageof the solar cell is given as follows:

Icell = Iph − ID −Vcell + RsIcell

Rp(1)

ID = Isat

exp

[ qKT

(Vcell + RsIcell)]− 1

. (2)

Fig. 2. Solar cell equivalent model

Fig. 3. P-V characteristics of NA-901 (WQ) 90W PV module

The power-voltage output of the Simulink model is shown inFig. 3, while the obtained I-V curves are shown in Fig. 4, refer-ence to the key specifications of the NA-901 module illustrated inTable 1 [7], the results of Simulink PV module show the excellentcorrespondence to the model.

Table 1. Key specifications of the NA-901 PV moduleTemperature T 25 CMaximum power Pmax 90 Wp

Open-circuit voltage Vα 65.2 VShort-circuit current Isc 2.11 AVoltage, max power Vmpp 49.3 VCurrent, max power Impp 1.83 A

3. Design and modeling of the buck converter

A dc-dc converter is used to increase the efficiency of the sys-tem by matching the supplied voltage to the voltage required bythe load.

In our application, the output voltage must be kept constant,regardless of changes in the input voltage due to variation in cli-matic conditions, or in the effective load. This is accomplishedby building a circuit that varies the converter control input, insuch a way that the output voltage is regulated to be equal to adesired reference voltage.

Fig. 4. I-V characteristics of NA-901 (WQ) 90W PV module

Fig. 5. Circuit diagram of buck converter

The modeling begins as usual, by determining the voltage andcurrent waveforms of the inductor and capacitor (Fig. 5).

The operating mode of a buck converter circuit can be dividedinto two modes. Mode 1 begins when the switch is in position1, the circuit of Fig. 6(a) is obtained. The current flow throughinductor L, diode D, capacitor C.

In mode 2, the switch is in position 2, the circuit of Fig. 6(b)is obtained. During this mode, the energy stored in the capacitoris then transferred to the battery. Therefore, the output voltage isless than the input voltage and is expressed as:

Vbat = DVpv (3)

Where D represent the duty cycle.

4. Battery model

The battery model was based on a lead-acid battery PSpicemodel [8]. Lead-acid battery cells consist of two plates, positiveand negative immersed in a dilute sulfuric acid solution. The pos-itive plate, or anode, is made of lead dioxide (PbO2) and the nega-tive plate, or cathode, is made of lead (Pb). The battery model hastwo modes of operation: charging and discharging. The batteryis in the charging mode when the current flowing into the batteryis positive and discharging mode when the current is negative.

The terminal voltage of the battery is given by:

Vbat = V + RIbat. (4)

Where V and R are governed by a different set of equations de-pending on which operating mode of the battery is in.

5. DC-DC regulator system

A block diagram of a typical DC-DC system incorporating abuck converter and feedback loop is illustrated in Fig. 8.

A Proportional Integral Derivative controller (PID) compen-sator is used to maintain a constant dc voltage of 48V in converter

Amatoul et al./Information Sciences and Computer Engineering, Vol. 2, No. 2, 2011 3

(a)

(b)

Fig. 6. Buck converter circuit: (a) when the switch is in position 1, (b) when theswitch is in position 2.

Fig. 7. Battery model [6]

output. It is desired to design this feedback system in such a waythat the output voltage is accurately regulated, and is insensitiveto disturbances in PV voltage or in the load current. In addition,the feedback system should be stable, and properties such as tran-sient overshoot, setting time, and steady-state regulation shouldmeet specifications. [9]

To design the system of Fig. 8, we need a dynamic modelof the switching converter. To develop this dynamic model, wewill extend the steady-state models to include the dynamics intro-duced by the inductor and capacitor of the converter. Simplifiedterminal equations of the component elements are used.

LdiL (t)

dt= Dvpv (t) − v (t) .

Cdv (t)

dt= iL (t) − v (t)

R.

(5)

[ diL(t)dt

dv(t)dt

]=

[0 − 1

L1C − 1

RC

] (iL (t)v (t)

)+

[ DL0

]vpv (t) . (6)

Now apply standard linearization technique and apply pertur-bations as follows:

Fig. 8. DC-DC regulator system including a buck converter power stage and afeedback network

d∧iL

(t)

dtd∧v (t)dt

=[

0 − 1L

1C − 1

RC

] ∧iL

(t)∧v (t)

+[

DL

Vpv

L0 0

] ∧vpv

(t)∧d (t)

.(7)

vpv (t) = V+pv∧vpv

(t) ,

d (t) = D +∧d (t) ,

⟨iL(t)⟩ = IL +∧iL

(t) ,

v (t) = V +∧v (t) .

(8)

The line-to-output transfer function is

Gvd (s) =Vpv

11 + s L

R + s2LC

. (9)

Gvd (s) =∧v (s)∧d (s)

∣∣∣∣∣∣∣∣ ,∧vpv(s)=0

(10)

Thus, the line-to-output transfer function contains a DC gain Gg0and a quadratic pole pair:

Gvg (s) = Gg01

1 + sQω0+

(sω0

)2 . (11)

Analytical expressions for the salient features of the line-to-output transfer function are found by equating like terms in (9)and (10). The DC gain is

Gg0 = Vpv. (12)

By equating the coefficients of s2 and of s in the denominators of(9) and (10), one obtains

ω0 =1√

LC. (13)

and Q = R

√CL. (14)

For simulation, the following values are used to simulate thebuck converter.

Vout = 48VL = 2.5mH,C = 25µF,R = 20Ω,Vpv = 197.2V.(15)

4 Amatoul et al./Information Sciences and Computer Engineering, Vol. 2, No. 2, 2011

The Bode diagram of a typical loop transfer function is shown inFig. 9. The gain margin and the phase margin are easily visual-ized in the Bode plot.

Fig. 9. Bode plot of the loop transfer function Gvg(s) before correction

It is desirable to have high gain at low frequency and rapidlydecreasing gain after the gain crossover frequency. Since we re-quire that the closed loop system should be stable, the slope ofthe gain curve at crossover cannot be too steep at the crossover.However, the phase of a system is related to its gain, and hence itis not possible to independently specify these quantities.

As illustrated in Fig. 9, the system does not have enough phaseand gain margins which can influence the stability and the speedof the system. Consequently the voltage regulator must compen-sate for this lack of phase without destabilizing the system, thusby guaranteeing a good rejection of disturbance.

A guideline in PID control system design is to ensure a 3–10dBgain margin and 20 phase margin. Here, it must be noted that3dB and 20 are the endurable minimum values, and that whenthese values are chosen, control systems are usually very oscil-latory and can easily become unstable. If satisfactory dampingand robustness are expected, a phase margin (∆φ) of greater than50is recommended.

The PID controller in the continuous time domain is describedby

Gc (s) = Gc0

(1 + s

ωz

) (1 + ωL

s

)(1 + s

ωp

) . (16)

Where

ωz = ωc

√1 − sin(∆φ)1 + sin (∆φ)

. (17)

Gc0 =

(ωc

ω0

)2 1T0

√ωz

ωp. (18)

ωp = ωc

√1 + sin(∆φ)1 − sin (∆φ)

. (19)

ωc is the cut-off frequency of the system.

Fig. 10. Bode plot of the loop transfer function Gvg(s) after correction

It is clear that closed loop PID controlled buck converter givesimproved transient and steady state performance and succeededin to add more phase margin.

6. Simulations and results

In this work a PID compensator is used to maintain a constantbus voltage of 48V in converter output, irrespective of variationsin climatic conditions and load. The PID compensator minimizessteady state error to zero.

For whole system simulation is used Matlab/Simulink.

Standard test conditions (T = 25C and G = 1000W/m2) withconstant load resistance

The simulation results have been obtained under standard cli-matic conditions (T = 25C and G = 1000W/m2). It can beclearly seen that, in steady state, the DC link voltage is main-tained at reference.

Change of climatic conditions with constant load resistanceFig. 12 presents the evolution of some characteristics of the

system during a variation transient in solar radiation betweent=0.4s and t=0.6s for G=200W/m2. It can be seen that the reg-ulation of the DC link voltage is maintained at a constant levelVref=48V, It has to be said that this is an extreme change in so-lar radiation levels that is unlikely to occur but shows the goodperformance of the controller.

Standard test conditions (T = 25C and G = 1000 W/m2) withvarying load resistance

Fig. 13 presents a zoom-view of characteristics of the systemduring a variation transient in load resistance between t = 0.06s,R = 82Ω and t = 0.1s, R = 20Ω for G = 1000W/m2. The outputvoltage is achieved quickly after the transient period followingeach change in values of load resistance.

For all the results above, the DC-DC regulator system includ-ing a buck converter power stage and a feedback network is ableto maintain the output voltage at the reference voltage and robustto the variation of the external conditions.

Amatoul et al./Information Sciences and Computer Engineering, Vol. 2, No. 2, 2011 5

Fig. 11. Simulation results under Standard test conditions and constant load re-sistance

7. Conclusion

Photovoltaic system, DC-DC buck converter, DC-DC regula-tor and battery models have been described. From the proposeddesign, the buck converter is able to produce a constant outputvoltage of 48V from an inconstant PV array voltage Simulationstudies demonstrate that the use of a simple DC-DC buck con-

Fig. 12. Simulation results under change of climatic conditions and constant loadresistance

verter gives better adaptability to the variable radiation condi-tions, and the optimized parameters of PID controllers show abetter response curve to control the output voltage. Therefore, itcan be attach to a grid connected system, as developed in [10],for future works.

The DC solution features a simpler and more robust primarycontrol, as compared to AC micro-grids, where the controlis much more complex because it has to consider active andreactive power flaw and phase synchronization or phase loss [11].

6 Amatoul et al./Information Sciences and Computer Engineering, Vol. 2, No. 2, 2011

Fig. 13. Simulation results under Standard test conditions with varying load re-sistance

References

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[6] R. A. Messenger and J. Ventre, Photovoltaic Systems Engineering.CRC Press, 2nd ed., 2004.

[7] http://www.solartec.gr/pdf/panels/sharp na series90w 85w.pdf.[8] L. Castaner and S. Silvestre, Modelling Photovoltaic Systems Us-

ing Pspice. John Wiley and Sons Ltd, 2002.[9] R. W. Erickson and D. Maksimovic, Fundamentals of Power Elec-

tronics. Springer, 2nd ed., 2000.[10] F. Z. Amatoul, M. T. Lamchich, and O. Abdelkader, “Design con-

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Fatima Zahra Amatoul has submitted her thesisin electric engineering to the Faculty of Scienceand Techniques of Marrakech in in September2005, and received her Masters degree in De-cember 2007 from the Faculty of Sciences Sem-lalia at Marrakech. Currently, she is doing her

PhD (in her third year) at Faculty of Science and Techniques of Mar-rakech. Her research interest area is renewable energy sources control.

Moulay Tahar Lamchich has submitted his the-sis in electrotechnics in September 1991 andreceived his third cycle degree from the Fac-ulty of Sciences Semlalia at Marrakech. He re-ceived his PhD from the same university in July2000. He is presently Professor-ability at the

same Faculty, at the Department of Physics. His main activity is basedon short-circuit mechanical effects in substation structures and his re-search interests have included active power filters, machine drivers,static converters, and published several technical papers in this field.

Abdelkader Outzourhit holds a PhD degree inApplied Physics from the Colorado School ofMines, Golden, CO, USA. He is currently a pro-fessor of physics in the department of physics, ofthe Faculty of Sciences, Cadi Ayyad Universityin Marrakech, Morocco. His research is centred

on the energy conversion and storage and the coupling of renewable en-ergy sources with desalination systems. He has participated in severalEU-funded project and renewable energy and hybrid systems. He is thelocal responsible of the HYRESS project at the University.